An asynchronous generator is identical to an induction motor, in that the current inducing an electric current in the rotor is created by the external power supply. The key difference is that motor loads lag- if the syncronous frequency is 1800rpm, the motor would run maybe 1780rpm. But when it's spun at a higher rate (like 1850rpm, etc), it will create current in the stator as opposed to consume it.
If you're off-grid, an external source like batteries is still required. The talk about capacitors is that if there's some residual ferromagnatism in the rotor from previous magnetization, some current is generated in the stator, and that can be captured via the capacitors to induce greater magnetization in the coil.
